LISP I Programmer's Manual - Software Preservation Group

For example,1(a)(b)(,) - d e is written asFor further discussion of the smplfy function, seeGoldberg, Solomon H., "Solution of an Electrical Network usinga Digital ~omputer", S.M. Thesis, Course VI, M.I.T., August,1959distrb[e;p] : machine languageThe function dstrb will distribute conditionally theproducts of sums appearing in the expression e. The propositionp determines whether a given sum is to be distributed,Thus in the following example let the proposition p of a sumbe that "if y is included in a sum, do not distribute thissum", then(x+a ) (y+z+b ) (w+2)distributes to(xw) (y+z+b )+ (2x) (y+z+b)+ (aw) (y+z+b)+ (2a) (y+z+b)For the correct notation for sums and products in LISP seeabove under the function smplfy.diff [y;x] : machine languageThe function diff differentiates the algebraic expressiony, with respect to x. The value of diff is the (unsimplified)algebraic expression, . Gradients must be provided on3 xthe association lists of all the functions used in the expression,y, except for PLUS and TIMES. See the notation andreference given under smplfy.